Please see this thread for detailed instructions about how to get the State return to recognize the backdoor Roth contribution without applying the tax.
In addition, here is a TurboTax article with the steps for entering a Roth Backdoor conversion.
A backdoor Roth IRA allows you to get around income limits by converting a Traditional IRA into a Roth IRA. Contributing directly to a Roth IRA is restricted if your income is beyond certain limits, but there are no income limits for conversions.